This is the first course in the undergraduate abstract algebra sequence at OSU. In this course, we shall study the algebraic structures called groups, rings, and fields. Examples include the set of symmetries of a regular polygon, the set of polynomials with integer coefficients, and the complex numbers. While we will frequently think about such concrete examples, one aim of this course is to become familiar with abstract concepts and to prove theorems that apply in wide generality.
A strong emphasis will be placed on communicating mathematics clearly and effectively, especially in writing.
Max Kutler, kutler.8(at)osu(dot)edu.
Office: Math Tower 756
Office hours: Monday, Thursday, Friday 11 am-12 pm, and by appointment
Abstract Algebra: Theory and Applications by Tom Judson, 2022 edition (http://abstract.ups.edu/)
There will be two homework assignments due each week, typically on Tuesday and Friday.
Solutions must be written clearly, legibly, and with appropriate style. Among other things, this means your work should include proper grammar, punctuation, and spelling. I recommend using Guidelines for Good Mathematical Writing by Francis Su as a basic style guide.
You are encouraged to discuss the homework with other members of the class. If you do so, you should acknowledge their assistance on your submitted homework. Furthermore, you should feel free to use sources beyond your textbook, personal notes, and past homework when crafting your solutions. You must, however, cite any such sources, and you must write up all of your final solutions on your own.